Question

use the thin lens equation to explain why for a given screen-object distance there are two positions where the image is in focus

Answer 1

The the light rays follow the same path through a lens whether coming from the left or right - it is called the principle of reversibility. The lens can be turned around and would still work just the same. If the object is x cm from one side of the Lens and y cm from the other side, turning the lens around will simply reverse x and y values. The object-screen distance (x+y) is unchanged. So for a given object-screen distance, there are two positions where the image is in focus

Using several different measured object lengths and their corresponding image lengths, we will find the focal length of a lens, as well as verify the characteristics of the image (location, height, virtual or real, inverted or right-side up) for each object distance. This data will be used to prove that the thin lens equation is true.

Hypothesis and Rationale: By plotting the inverse of the object distances and the inverse of the corresponding image distances on a graph, the inverse of the x-intercept and the slope of the resulting graph will be equal to the focal length of our lens. We know this based on the equation 1/f=1/di + 1/do.

Methods and Materials: To do this experiment, we began with an optical bench which we placed on a flat surface (our desk). Then, we attached our object (the light source) to the optical bench where distance=0cm. It is important that we aimed the light source so that the image (ours was two parallel arrows) down the optical bench. This allows us to measure the object distance with ease. Then we placed a blank white screen on the opposite end of the optical bench from the light source where the image was facing. Finally, we placed a thin lens holder in the middle, and turned on the light source by plugging it into a power outlet. In order to get the data necessary, we placed the lens holder in a position that is between the light source and the screen, and moved the screen to a position where there was a clear image that is similar to the object on the light source (the image should be VERY CLEAR). We measured and recorded the distance of the lens holder from the light source(Do) as well as the lens holder from the screen(Di). Then we moved the lens holder to an other position between the light source and screen, found where the new image appeared with the screen and recorded the same measurements. We repeated this process for 10 specific and different locations of the lens holder, using these points to generate our graph.